What is (x+7)/(x+5)-(7x)/(x^2-3x-40) ?

The solution to (x+7)/(x+5)-(7x)/(x^2-3x-40) is (x^2-8x-56)/((x+5)(x-8))

Popular >

simplify (x+7)/(x+5)-(7x)/(x^2-3x-40)

simplify

\frac{x + 7}{x + 5} - \frac{7 x}{x ^{2} - 3 x - 40}

\frac{x ^{2} - 8 x - 56}{( x + 5 ) ( x - 8 )}

Solution steps

\frac{x + 7}{x + 5} - \frac{7 x}{x ^{2} - 3 x - 40}

Least Common Multiplier of

x + 5, x^{2} - 3 x - 40 : (x + 5) (x - 8)

Adjust Fractions based on the LCM

= \frac{( x + 7 ) ( x - 8 )}{( x + 5 ) ( x - 8 )} - \frac{7 x}{( x + 5 ) ( x - 8 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{( x + 7 ) ( x - 8 ) - 7 x}{( x + 5 ) ( x - 8 )}

Simplify

(x + 7) (x - 8) - 7 x : x^{2} - 8 x - 56

= \frac{x ^{2} - 8 x - 56}{( x + 5 ) ( x - 8 )}

(x - 3) (2 x + 1)

\frac{2 x ^{3} + 5 x ^{2} + 9}{x + 3}

- \frac{4}{7} + \frac{2}{7} x - 14 x + \frac{4}{7}

(2 x^{3} - 3 x^{2} + 5 x - 1) + (x^{2} + 1 - 3 x)

\frac{27 m ^{4} n ^{6} - 15 m ^{3} n ^{6} + 3 m n ^{2}}{3 m n ^{2}}

What is (x+7)/(x+5)-(7x)/(x^2-3x-40) ?
The solution to (x+7)/(x+5)-(7x)/(x^2-3x-40) is (x^2-8x-56)/((x+5)(x-8))